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A bill released Thursday repeal the deduction for state and local taxes

However, one modification allows itemized property tax deduction up to $10,000

Washington (CNN)House Republicans from New York and New Jersey aren't giving up their push to retain the deduction for state and local taxes, also known SALT, describing the newly released tax reform plan from GOP leaders as a starting point but vowing to keep up the fight to restore the popular tax break.

The new bill, which was released Thursday, eliminates most of the deduction, but still allows individuals to deduct up to $10,000 for property taxes. For tax writers, getting rid of SALT helps raise billions for tax cuts.

Drafters originally intended to scrap the property tax deduction all together, but after fierce pushback from lawmakers in high-tax states, Republican leaders decided to keep the tax break -- but with the $10,000 cap.

Still, that's not enough, some say, and they plan to keep fighting as the bill goes to committee markup next week.

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Rep. Frank LoBiondo of New Jersey, the state with the highest property taxes, said the $10,000 cap for property tax deductions -- in addition to the elimination of the state income tax deduction -- "would be detrimental to New Jersey residents."

"Thus, this bill is not something I could support in its current form," he said in a statement, adding that he's working with members from his state and New York on a counter-proposal to preserve the deductions.

Rep. Tom MacArthur of New Jersey said he's not opposed to the bill right now but he's still "trying to get to 'yes.'" One of the lead negotiators in the SALT debate, MacArthur said he wants the cap to move to $12,500 instead.

"That is the number that I believe captures all of the people," he told reporters.

Rep. Leonard Lance, another lead negotiator on SALT, described the bill as "unacceptable at this time" and pledged to keep up the talks. "We have made some progress but more needs to be done," he said in a statement.

Republican leaders are urging members to focus on the bigger picture, arguing that with the doubling of the standard deduction and other changes, like the elimination of the alternative minimum tax and the increase in the child tax credit, would help provide a net benefit to taxpayers -- even if they lost deductibility on other taxes.

Rep. Peter Roskam of Illinois sits on the ways and means committee, which drafted the bill, and said he feels it will be good for people in high-tax states like his.

"They're interested in tax relief, they're not particularly concerned about the equation by which that relief gets to that," he said. "And I'm confident that this product today ... gives my constituents that tax relief."

Much of the New York contingent was more vocal about the complete removal of the state income tax deduction. Rep. Lee Zeldin flat out said he was a "no" to the bill in its current form.

Rep. Claudia Tenney also of New York put out a statement saying "the SALT deduction matters" in a state with high taxes like her state. She described the bill as "only the start of the tax reform conversation" and promised to keep advocating to keep SALT in place.